论文标题
Dvoretzky型定理，用于希尔伯特空间的本地有限子集
Dvoretzky-type theorem for locally finite subsets of a Hilbert space
论文作者
论文摘要
本文的主要结果：给定任何$ \ varepsilon> 0 $，$ \ ell_2 $的每个本地有限子集都允许$（1+ \ varepsilon）$ - bilipschitz嵌入任意的无限少量班克空间。 结果是基于两个具有独立关注的结果： （1）两个有限维欧几里得空间的直接总和包含一个受控维度的子效果，该尺寸为$ \ varepsilon $ - 与$ 1 $ unconditional在二维空间中的$ 1 $ unccontional close。 （2）对于任何有限维的Banach Space $ y $及其直接的$ x $，就$ 1 $ $ x $而言，在二维空间中存在$ 1 $ - 条件的基础，存在$（1+ \ varepsilon）$ - bilipschitz-bilipschitz将$ y $嵌入$ y $中的$ x $中，与$ x $相结合，并在小球上构成了一定的标识。进入第二个求和。
The main result of the paper: Given any $\varepsilon>0$, every locally finite subset of $\ell_2$ admits a $(1+\varepsilon)$-bilipschitz embedding into an arbitrary infinite-dimensional Banach space. The result is based on two results which are of independent interest: (1) A direct sum of two finite-dimensional Euclidean spaces contains a sub-sum of a controlled dimension which is $\varepsilon$-close to a direct sum with respect to a $1$-unconditional basis in a two-dimensional space. (2) For any finite-dimensional Banach space $Y$ and its direct sum $X$ with itself with respect to a $1$-unconditional basis in a two-dimensional space, there exists a $(1+\varepsilon)$-bilipschitz embedding of $Y$ into $X$ which on a small ball coincides with the identity map onto the first summand and on a complement of a large ball coincides with the identity map onto the second summand.
